There's two distinct sides to this question: how does carbon fiber the material fare the way it's used in modern road bikes, and how do carbon road bikes with the features they almost all have fare.
Carbon road bikes, as they actually exist for the most part, are excellent at being structurally strong against all the typical loads on a bike, but are relatively vulnerable to incidental damage compared to metal bikes. It's relatively easy for permanent damage to be done by piercing, denting, gouging, or abrading contact against frame members. It also takes relatively less unintentional cyclic tire, cable, or rider contact with frame members to wear significant amounts of material away.
If your commutes mimic the type of recreational, sporty riding that carbon road bikes are really designed for, you're less likely to encounter issues from any of these weaknesses. If you've got more "real world" type risk factors, for example the need to leave the bike locked up on a city street where anyone can lock up next to it and gouge it with a pedal, carbon can be a liability. If the bike's economics as a means of transportation has meaning to you, i.e. if you need it to get around and replacing it if damaged would be a huge burden, carbon easily becomes an outright bad choice compared to a steel bike with none of the aforementioned toughness/fragility issues, much lower cost, and negligibly less performance.
A second factor is that the integrated headsets and various press-fit BBs now found on most carbon road bikes, and especially BB30, were really never intended to be low-maintenance and long-lived in real-world conditions, and especially with regular exposure to rain and grit. They have inferior sealing and tend to develop creaks and/or wear out quickly compared to pressed headsets and threaded shells. If you live someplace dry, these concerns are lessened. Everywhere else, they are terrible features for a commute bike.
